Rémy Dubertrand

Many-body semiclassics for Bose-Hubbard: spectral statistics and random wave approach

Semiclassical techniques from quantum chaos have been recently generalised to describe many-body interacting bosonic systems written as second quantised models. To understand the emergence of new phenomena due to many-body coherent effects I will first motivate how to build a quantum/classical correspondence, and how to follow the semiclassical program from there. This will be used first to state when universal spectral appear in Bose-Hubbard models. Then I will explain how to describe the eigenstates using a statistical perspective. This involves more precisely the connection with Random Matrix Theory and Berry’s ansatz of random superpositions of Fock states respectively. In particular it will be discussed how to use it in order to tackle the issue of thermalisation in isolated systems.